I would have put dormir in the imperfect tense, since in the context of the paragraph this person has had an ongoing problem, but as you can see it is in the preterite. Would it have been terribly incorrect to have put in in the imperfect?

No recuerdo la última noche en que dormía bien.
I don’t remember the last night when I was sleeping well.

__________________Lo propio de la verdad es que se basta a sí misma, aquel que la posee no intenta convencer a nadie."An enemy is somebody who flatters you. A friend is somebody who criticizes the living daylights out of you."

Imperfect would have been quite wrong for first person. From the point of view of a person each instance of sleeping has definite beginning and end (to fall asleep and to wake up). By its own nature "la última noche en que dormí bien" has very definite boundaries.

You can say

No recuerdo la última noche en que (él/ella) dormía bien.

as a matter of context. For you sleeping is not an action with beginning and end but some circumstances when you were aware of the way she or he was sleeping.

(But as a matter of fact, I always sleep very well... so probably I'd never say any of these in a month of Sundays... but you'll never know...)

__________________Lo propio de la verdad es que se basta a sí misma, aquel que la posee no intenta convencer a nadie."An enemy is somebody who flatters you. A friend is somebody who criticizes the living daylights out of you."

__________________Lo propio de la verdad es que se basta a sí misma, aquel que la posee no intenta convencer a nadie."An enemy is somebody who flatters you. A friend is somebody who criticizes the living daylights out of you."